Two
years ago, astrophysicists studying Type Ia supernovas discovered that our
universe is a much stranger place than we had imagined, with invisible vacuum
energy accelerating its expansion.(See
my column about this in the May-1999 Analog.)
However, new astrophysical observations from the BOOMERanG experiment (BalloonObservations Of Millimetric
Extragalactic Radiation and Geomagnetics), a
balloon-borne cryogenic microwave telescope measurement that flew at an
altitude ofabout 24 miles over the
Antarctic, indicate that our universe is also rather ordinary, in that its
space is maximally flat.The term
“flat” as used here means that the space of our universe is neither positively
curved like a ball or negatively curved like a potato chip.It appears that in our universe, the
tendencies of space toward positive curvature from gravitational attraction and
towards negative curvature from expansion kinetic energy are precisely in
balance, leaving space on the average completely free of curvature.

In
general relativity the curvature of space is characterized by the density
parameter Wtotal , which is less than 1 for negative curvature, greater than
1 for positive curvature, and exactly one for flat uncurved space.The BOOMERanG measurement has shown that Wtotal = 1.00 ± 0.12.There are theoretical reasons for taking
this as an indication that Wtotal is precisely 1.

Our
present “standard model” view of Big Bang cosmology tells us that about 14
billion years ago the Big Bang started from a tiny point that explosively
unfolded to make what became our universe.In the first few picoseconds of the Big Bang, for reasons that are not
understood, the universe expanded very rapidly in a process described as
“exponential inflation”.During this
inflationary period, the diameter of the universe increased much faster than
the speed of light.Then the expansion
slowed, and the universe passed through phases in which the four forces
(strong, weak, electromagnetic, and gravitational) separated, changed
strengths, and resolved themselves, in which quarks and leptons formed and
acquired mass, in which composite particles including protons and neutrons
formed from the quarks, and in which the protons and neutrons combined to form
primordial nuclei of deuterium, helium 3 and 4, and lithium 6 and 7.

Finally,
about 300,000 years after the initial Big Bang, the universe had cooled enough
to allow the positively charged protons and heavier nuclei to combine with the
negatively charged electrons to form neutral atoms.At this point the “primordial soup” of the universe became
electrically neutral.Photons of light
in the medium, which up to that time had been trapped by rapid and repeated
absorption and scattering with the surrounding charged particles, abruptly
found themselves in a transparent medium.They became free particles, able to travel large distances without
interactions.

For
the most part, these photons have been traveling through the universe since
that time without scattering.However,
the expansion of the universe has stretched their wavelengths by a factor of a
thousand.They reach us now, 14 billion
years later, as very low energy photons of the cosmic microwave background.Their wavelength distribution, originally
produced by the very hot plasma of the early universe, is now characteristic of
a cold “object” with a temperature that is only 2.73o above absolute
zero.

This
cosmic background radiation (CBR) from the Big Bang was first detected in the
1960s.It has been repeatedly measured
with increasing precision for the last four decades, culminating with the COBE
satellite measurements in the early 1990s.However, in the past five years it has been realized that the CBR has
encoded within it some definitive information about the characteristics and
composition of our universe.We are
only now, through BOOMERanG and similar measurements, gaining the capability of
decoding that information.

Theoretical
studies have shown that as the early universe expanded, sound waves propagated
through the dense medium that closed back on itself, so that the hypersphere of
the universe rang like a bell.The
detailed frequency spectrum of the sound waves that permeated the primordial universe,
literally the sounds of the Big Bang, depends on details such as the expansion
rate, the energy balance, and the matter density of the universe at the early
age of 300,000 years.

But
how could one possibly listen to sound waves that had dwindled away and died 14
billion years ago?Fortunately, there
is a way.The primordial sound waves
were present at the time that light decoupled from matter to form the CBR.The sound waves, because they produced
regions of compression and rarefaction in the medium, modulated the CMB, with
some regions being slightly hotter or colder than other.This modulation is predicted to still be
present in the CBR at a scale of less than 2 degrees in angle.Basically, to see the effects of the
primordial sound waves one must look for variations in the temperature of the
CBR of about 1 part in a ten thousand through a peephole that spans a cone in
the sky with an opening angle of 2 degrees or less, and scan this peephole
across the sky.

Unfortunately,
this modulation effect had not been predicted when the COBE measurement was
designed, and so that measurement had an angular resolution of about 7 degrees
in angle, a resolution that averaged away all of the crucial information.Therefore, it was realized about five years
ago (see my column on the 17th Texas Symposium in the August-95 Analog)
that a whole new set of CMB measurements was needed, and that these would place
very tight constraints on the parameters of the universe.

BOOMERanG
is one of these new measurements.It is
an international scientific collaboration of astrophysics groups based in Rome,
London, Pasadena, Berkeley, Florence, Geneva, Santa Barbara, Lisbon, Paris,
Amherst, and Toronto.Because of a
combination of careful design and good luck, the BOOMERanG measurements have
significantly improved our knowledge of the parameters of the universe.

BOOMERanG
consists of a microwave telescope that focuses and concentrates the microwave
radiation from a sky-angle of 0.2 degrees on three cryogenic Si3N4
web detectors that are sensitive to frequencies of 90 GHz, 150 GHz, and 240
GHz, respectively.The webs change
temperature in response to the energy delivered by the focused microwaves.The entire device is mounted between shields
that blocked the radiation from the Earth and the Sun.The sensitive aperture of the telescope is
scanned over the sky, providing a 3-frequency image of the sky mapped into
about 45,000 pixels in each frequency channel.

The telescope was lifted from McMurdo
Station in Antarctica to the outer fringes of the atmosphere at an altitude of
120,000 ft by a large 2.8 × 107
ft3 helium-filled balloon.The instrument remained there, gathering data over a patch of sky with
an angular area of 1800 square degrees, for a period of 10.8 days between
December 29, 1998 and January 9, 1999.The balloon followed a circular path centered at the South Pole, and
returned to within 80 miles of its launch site.There the telescope was cut down and retrieved.

The raw data produced by BOOMERanG is
a time sequence of signals in each frequency channel consisting of 5.4 × 107 16-bit samples per channel.This sequence had to be converted by data
analysis, first into a sky map of temperature variations at the parts in 10,000
level, and then by Fourier analysis into a distribution of the spatial
frequencies or angular sizes of the observed variations.It is these distributions that can be
compared with models of the early universe.If the universe if “flat”, in the sense defined above, then the angular
size is expected to have a peak at about 1.8 degrees.This corresponds to a “standing” sound wave in the early universe
that has a number of maxima and minima (or “multipolarity”) L in its pattern of
compression and rarefaction that is L=197±6
or about 200.

From
calculations of the standing sound waves in the early universe, it is found
that the value of L is directly related to the flatness or curvature of the
universe.For example, L=125 would
correspond to an open universe with negative “potato-chip” curvature and with Wtotal = 0.66.On the other hand, L=300 would correspond to an closed universe with
positive spherical curvature and with Wtotal = 1.55.The
observed value of L=200 is precisely what is expected for a flat universe with Wtotal = 1.0.Therefore, BOOMERanG has accomplished a remarkable feat.It has “heard” the sound of a perfectly flat
Big Bang from a distance of 14 billion light years!

But
there is also another important aspect to the BOOMERanG measurements.The data on the accelerating expansion of the
universe from studies of Type Ia supernovas mentioned above places certain
constraints on the parameters describing the universe, the age T0 of
the universe, the total density parameter Wtotal, the matter density WM, and the vacuum energy density WL.The BOOMERanG measurements place other
constraints on the same quantities.And, plotted on an appropriate diagram, these constraints form an “X”,
with the cross point indicating the parameter values that are consistent with
both measurements.

These
lead to the conclusions that the universe has an age T0= 14
billion years, Wtotal = 1, WM, = 0.3 and WL = 0.7.The surprisingly large value of WL, which implies the dominance of vacuum
energy in over normal mass-energy and dark matter mass-energy in the universe
at present, is a result that rocked the astrophysics community two years
ago.This is now supported by the
BOOMERanG results, which come at placing constraints on the parameters from a completely
different direction.

We
now understand that the space of our universe is flat, that it is expanding at
an ever-increasing rate, and that it will never re-collapse to a “Big
Crunch”.What we don’t understand is
why.But physicists, astronomers, and
astrophysicists around the world are working on that question too.

Afterword (September 21, 2003):
One of the readers of this column asked if the "Sound of the Big Bang" mentioned
in the title is actually recorded anywhere, so that one can listen to it.
The short answer is "no", but the question set me to thinking: "Why not?"
The spectrum of frequencies at which the universe was acting as a resonator has
been well measured by BOOMERanG and more recently by WMAP. I'm an
experienced user of the symbolic algebra program Mathematica, which provides the
user with the capability of making mathematical functions into sound.

So yesterday morning I sat down and wrote a 16 line
Mathematica notebook that produces a simulation of the "sound of the Big Bang",
based on WMAP data. I used their power spectrum to combine a set of sine
waves with amplitudes equal to the histogram areas of their points, modulated
this with the measured profile of the emission of the original cosmic background
radiation (center = 376,000 years = 50 seconds of simulation, width = 118,000
years = 15.7 seconds of simulation.), and shifted the frequencies down as time
to the 2/3 power, the rate of growth of the radius of the universe in the early
Big Bang.

The resulting simulated sound of the Big Bang can
be heard HERE
using a browser that supports .wav sound files, or can be downloaded and played
on a media player. There is also an mpeg version dowloadable HERE. It sounds rather like a large jet plane 100 feet off
the ground flying over your house in the middle of the night. You can hear
the falling frequencies as the universe expands and becomes more of a bass
instrument, the rise and fall of CMB emission, and the interesting counterplay
of the frequencies that were measured. It's what you might hear if you
could "listen" to the cosmic background radiation during the first 760,000 years
of the birth of the universe.